Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Visual Computing Center (VCC)
Computer Science Program
Date
2012-01Preprint Posting Date
2011-06-07Permanent link to this record
http://hdl.handle.net/10754/562040
Metadata
Show full item recordAbstract
Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identification of circle families on a given cyclide and for the direct design of those. In particular, we show that certain triples of circle families may be arranged as so-called hexagonal webs, and we provide a complete classification of all possible hexagonal webs of circles on Darboux cyclides. © 2011 Elsevier B.V. All rights reserved.Citation
Pottmann, H., Shi, L., & Skopenkov, M. (2012). Darboux cyclides and webs from circles. Computer Aided Geometric Design, 29(1), 77–97. doi:10.1016/j.cagd.2011.10.002Publisher
Elsevier BVJournal
Computer Aided Geometric DesignarXiv
1106.1354Additional Links
http://arxiv.org/abs/arXiv:1106.1354v1ae974a485f413a2113503eed53cd6c53
10.1016/j.cagd.2011.10.002